Linear State space theory in the white noise space setting Academic Article uri icon

abstract

  • We study state space equations within the white noise space setting. A commutative ring of power series in a countable number of variables plays an important role. Transfer functions are rational functions with coefficients in this commutative ring, and are characterized in a number of ways. A major feature in our approach is the observation that key characteristics of a linear, time invariant, stochastic system are determined by the corresponding characteristics associated with the deterministic part of the system, namely its average behavior. Subjects: Probability (math. PR); Classical Analysis and ODEs (math. CA) MSC classes: 93E03, 60H40, 46E22, 47B32 Cite as: arXiv: 0911.2574 [math. PR](or arXiv: 0911.2574 v1 [math. PR] for this version) Submission history From: Daniel Alpay A [view email][v1] Fri, 13 Nov 2009 09: 20: 12 GMT (16kb)

publication date

  • January 1, 2009